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21 
Optimization of network mesh topologies and link capacities for congestion relief / D. de VilliersDe Villiers, Daniel January 2004 (has links)
Network design problems usually include the selection of nodes and arcs from lists of
potential sets to accomplish certain desirable properties. Foremost is often the capability
to accommodate the flow demands at a reasonable cost. In many applications it is also
imperative to have builtin reliability or survivability of the network. Delays of traffic are
undesirable since it affects Quality of Service (QoS) to clients of the network. It is seldom
possible to start a design for a new network and have the luxury of designing topology as
well as the optimal flow(routing). In this dissertation we consider the construction of a
network optimization system. This system may be used in the planning of network mesh
topologies and link capacities to avoid costly designs and congestion or to give advice on
congestion relief in existing networks.
This is done by selecting parts of a network that may be prone to congestion and model
this part by using mixed integer programming techniques. These models are then solved
by using a software product called CPLEX and various facilities are built into the decision
support system to allow the decision maker to experiment with some topological and flow
requirement changes. / Thesis (M.Sc. (Computer Science))NorthWest University, Potchefstroom Campus, 2005.

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Experimental models for network mesh topologies with designs that enhance survivability / John Mugambwa SerumagaZakeSerumagaZake, John Mugambwa January 2006 (has links)
Network design problems involving survivability usually include tradeoff of the potential for lost
revenues and customer goodwill against the extra costs required to increase the network
survivability. It also involves selection of nodes and edges from lists of potential sets to accomplish
certain desirable properties. In many applications it is imperative to have builtin reliability or
survivability of the network. Delays of traffic are undesirable since it affects quality of service (QoS) to clients of the network.
In this dissertation we consider the construction of an optimization system for network design with
survivability properties that may help in the planning of mesh topologies while maintaining a
certain degree of survivability of the network. This is done by providing for at least two diverse
paths between certain "special" nodes to provide protection against any single edge or node failure.
This part is modelled by using mixed integer programming techniques. A software product called
CPLEX then solves these models and various facilities are built into the decision support system to
allow the decision maker to experiment with some topological and flow requirement changes. / Thesis (M.Sc. (Computer Science))NorthWest University, Potchefstroom Campus, 2007

23 
Resident Scheduling ProblemRamahi, Muhannad Hasan 12 April 2012 (has links)
This thesis is concerned with the Resident Scheduling Problem (RSP) in which a good schedule is desired that will meet both departmental requirements and residents' preferences. Three scenarios that represent most situations and account for various departmental requirements and needs are described. Although similar scheduling problems are considered in the literature, no analysis exists that adequately deals with this specific problem. The problem is modeled as a mixedinteger program (MIP) and heuristic solution procedures are developed for the different identified scheduling scenarios. These procedures exploit the network structure of the problem which is an important feature that enhances problem solvability. For the sake of comparison, the problem is also solved exactly via the CPLEXMIP package. The contribution of this work is important since many hospitals are still utilizing manual techniques in preparing their own schedules, expending considerable effort and time with less scheduling flexibility. / Master of Science

24 
Mathematical Programming Approaches to the ThreeGroup Classification ProblemLoucopoulos, Constantine 08 1900 (has links)
In the last twelve years there has been considerable research interest in mathematical programming approaches to the statistical classification problem, primarily because they are not based on the assumptions of the parametric methods (Fisher's linear discriminant function, Smith's quadratic discriminant function) for optimality. This dissertation focuses on the development of mathematical programming models for the threegroup classification problem and examines the computational efficiency and classificatory performance of proposed and existing models. The classificatory performance of these models is compared with that of Fisher's linear discriminant function and Smith's quadratic discriminant function. Additionally, this dissertation investigates theoretical characteristics of mathematical programming models for the classification problem with three or more groups. A computationally efficient model for the threegroup classification problem is developed. This model minimizes directly the number of misclassifications in the training sample. Furthermore, the classificatory performance of the proposed model is enhanced by the introduction of a twophase algorithm. The same algorithm can be used to improve the classificatory performance of any intervalbased mathematical programming model for the classification problem with three or more groups. A modification to improve the computational efficiency of an existing model is also proposed. In addition, a multiplegroup extension of a mathematical programming model for the twogroup classification problem is introduced. A simulation study on classificatory performance reveals that the proposed models yield lower misclassification rates than Fisher's linear discriminant function and Smith's quadratic discriminant function under certain data configurations. Data configurations, where the parametric methods outperform the proposed models, are also identified. A number of theoretical characteristics of mathematical programming models for the classification problem are identified. These include conditions for the existence of feasible solutions, as well as conditions for the avoidance of degenerate solutions. Additionally, conditions are identified that guarantee the classificatory noninferiority of one model over another in the training sample.

25 
Limit and shakedown analyses by the pversion femNgo, Ngoc Son, Civil & Environmental Engineering, Faculty of Engineering, UNSW January 2005 (has links)
This thesis provides a contribution towards a general procedure for solving robustly and efficiently limit and shakedown analyses of engineering structures within the static approach which has been chosen for its simplicity of implementation. Throughout the thesis, attempts at improving the robustness and efficiency of the computations are presented. Beginning with efforts to prevent volumetric locking, which is a severe shortcoming of traditional low order htype displacement elements, the investigation proposes the use of the high order pversion of the finite element method. It is shown theoretically and confirmed numerically that this pmethod is not only robust in preventing locking, but also provides very accurate results. However, the use of uniformly distributed high order pelements may be computationally demanding when the size of the problem becomes large. This difficulty is tackled by two main approaches: use of a padaptive procedure at the elastic computation stage and use of approximate piecewise linear yield functions. The padaptive scheme produces a nonuniform pdistribution and helps to greatly reduce the number of degrees of freedom needed while still guaranteeing the required level of accuracy. The overall gain is that the sizes of the models are reduced significantly and hence also the computational effort. The adoption of piecewise linear yield surfaces helps to further increase the efficiency at the expense of possibly slightly less accurate, but still very acceptable, results. Stateoftheart linear programming solvers based on the very efficient interior point methodology are used. Significant gains in efficiency are achieved. A heuristic, semiadaptive scheme to piecewise linearize the yield surfaces is then developed to further reduce the size of the underlying optimization problems. The results show additional gains in efficiency. Finally, major conclusions are summarized, and various aspects suitable for further research are highlighted.

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Advances in Portfolio Selection Under Discrete Choice Constraints: A Mixedinteger Programming Approach and HeuristicsStoyan, Stephen J. 03 March 2010 (has links)
Over the last year or so, we have witnessed the global effects and repercussions related to the field of finance. Supposed blue chip
stocks and wellestablished companies have folded and filed for bankruptcy, an event that might have thought to been absurd two
years ago. In addition, finance and investment science has grown over the past few decades to include a plethora of investment options and regulations. Now more than ever, developments in the field are carefully examined and researched by potential investors. This thesis involves an investigation and quantitative analysis of key money management problems. The primary area of interest is Portfolio Selection, where we develop advanced financial models that are designed for
investment problems of the 21st century.
Portfolio selection is the process involved in making large investment decisions to generate a collection of assets. Over the
years the selection process has evolved dramatically. Current portfolio problems involve a complex, yet realistic set of
managing constraints that are coupled to general historic risk and return models. We identify three wellknown portfolio problems
and add an array of practical managing constraints that form three different types of MixedInteger Programs. The product is
advanced mathematical models related to riskreturn portfolios, index tracking portfolios, and an integrated stockbond portfolio selection model. The numerous sources of uncertainty are captured
in a Stochastic Programming framework, and Goal Programming techniques are used to facilitate various portfolio goals. The designs require the consideration of modelling elements and variables with respect to problem solvability. We
minimize tradeoffs in modelling and solvability issues found in the literature by developing problem specific algorithms. The algorithms are tailored to each portfolio design and involve decompositions and heuristics that improve solution speed and quality. The result is the generation of portfolios that have intriguing financial outcomes and perform well with respect to the market.
Portfolio selection is as dynamic and complex as the recent economic situation. In this thesis we present and further develop
the mathematical concepts related to portfolio construction. We investigate the key financial problems mentioned above, and
through quantitative financial modelling and computational implementations we introduce current approaches and advancements in field of Portfolio Optimization.

27 
Advances in Portfolio Selection Under Discrete Choice Constraints: A Mixedinteger Programming Approach and HeuristicsStoyan, Stephen J. 03 March 2010 (has links)
Over the last year or so, we have witnessed the global effects and repercussions related to the field of finance. Supposed blue chip
stocks and wellestablished companies have folded and filed for bankruptcy, an event that might have thought to been absurd two
years ago. In addition, finance and investment science has grown over the past few decades to include a plethora of investment options and regulations. Now more than ever, developments in the field are carefully examined and researched by potential investors. This thesis involves an investigation and quantitative analysis of key money management problems. The primary area of interest is Portfolio Selection, where we develop advanced financial models that are designed for
investment problems of the 21st century.
Portfolio selection is the process involved in making large investment decisions to generate a collection of assets. Over the
years the selection process has evolved dramatically. Current portfolio problems involve a complex, yet realistic set of
managing constraints that are coupled to general historic risk and return models. We identify three wellknown portfolio problems
and add an array of practical managing constraints that form three different types of MixedInteger Programs. The product is
advanced mathematical models related to riskreturn portfolios, index tracking portfolios, and an integrated stockbond portfolio selection model. The numerous sources of uncertainty are captured
in a Stochastic Programming framework, and Goal Programming techniques are used to facilitate various portfolio goals. The designs require the consideration of modelling elements and variables with respect to problem solvability. We
minimize tradeoffs in modelling and solvability issues found in the literature by developing problem specific algorithms. The algorithms are tailored to each portfolio design and involve decompositions and heuristics that improve solution speed and quality. The result is the generation of portfolios that have intriguing financial outcomes and perform well with respect to the market.
Portfolio selection is as dynamic and complex as the recent economic situation. In this thesis we present and further develop
the mathematical concepts related to portfolio construction. We investigate the key financial problems mentioned above, and
through quantitative financial modelling and computational implementations we introduce current approaches and advancements in field of Portfolio Optimization.

28 
An Improved Convex Optimization Model for TwoDimensional Facility LayoutJankovits, Ibolya 22 January 2007 (has links)
The facility layout design problem is a fundamental optimization problem encountered in many manufacturing and service organizations that was originally formulated in 1963 by Armour & Buffa. This thesis derives a convex programming model, IBIMODEL, that is designed to improve upon the ModCoAR model of Anjos & Vannelli for the facility layout problem with unequal areas. The purpose of IBIMODEL is to find 'good' initial locations for the departments that a second model then uses to produce a detailed solution to the facility layout problem. The proposed model has four ideas behind it: unlike ModCoAR, it does not improve the objective function as the departments start overlapping, it takes into account the aspect ratio requirements, it introduces a systematic approach to making parameter choices, and it uses a new second stage recently proposed by Luo, Anjos & Vannelli to obtain the actual facility layouts. In this way, IBIMODEL efficiently generates a reasonably diverse set of superior solutions that allow the second stage to provide a wide variety of layouts with relatively low aspect ratios and total cost.
The proposed methodology was implemented and numerical results are presented on wellknown large layout problems from the literature. To demonstrate the potential of the combination of IBIMODEL with Luo, Anjos & Vannelli's model, our results are compared with the best layouts found to date for these wellknown large facility layout problems. The results support the conclusion that the propose a methodology consistently produces competitive, and often improved, layouts for large instances when compared with other approaches in the literature.

29 
An Improved Convex Optimization Model for TwoDimensional Facility LayoutJankovits, Ibolya 22 January 2007 (has links)
The facility layout design problem is a fundamental optimization problem encountered in many manufacturing and service organizations that was originally formulated in 1963 by Armour & Buffa. This thesis derives a convex programming model, IBIMODEL, that is designed to improve upon the ModCoAR model of Anjos & Vannelli for the facility layout problem with unequal areas. The purpose of IBIMODEL is to find 'good' initial locations for the departments that a second model then uses to produce a detailed solution to the facility layout problem. The proposed model has four ideas behind it: unlike ModCoAR, it does not improve the objective function as the departments start overlapping, it takes into account the aspect ratio requirements, it introduces a systematic approach to making parameter choices, and it uses a new second stage recently proposed by Luo, Anjos & Vannelli to obtain the actual facility layouts. In this way, IBIMODEL efficiently generates a reasonably diverse set of superior solutions that allow the second stage to provide a wide variety of layouts with relatively low aspect ratios and total cost.
The proposed methodology was implemented and numerical results are presented on wellknown large layout problems from the literature. To demonstrate the potential of the combination of IBIMODEL with Luo, Anjos & Vannelli's model, our results are compared with the best layouts found to date for these wellknown large facility layout problems. The results support the conclusion that the propose a methodology consistently produces competitive, and often improved, layouts for large instances when compared with other approaches in the literature.

30 
Inverse Problems in Portfolio Selection: Scenario Optimization FrameworkBhowmick, Kaushiki 10 1900 (has links)
A number of researchers have proposed several Bayesian methods for portfolio selection, which combine statistical information from financial time series with the prior beliefs of the portfolio manager, in an attempt to reduce the impact of estimation errors in distribution parameters on the portfolio selection process and the effect of these errors on the performance of 'optimal' portfolios in outofsampledata.
This thesis seeks to reverse the direction of this process, inferring portfolio managers’ probabilistic beliefs about future distributions based on the portfolios that they hold. We refer to the process of portfolio selection as the forward problem and the process of retrieving the implied probabilities, given an optimal portfolio, as the inverse problem. We attempt to solve the inverse problem in a general setting by using a finite set of scenarios. Using a discrete time framework, we can retrieve probabilities associated with each of the scenarios, which tells us the views of the portfolio manager implicit in the choice of a portfolio considered optimal.
We conduct the implied views analysis for portfolios selected using expected utility maximization, where the investor's utility function is a globally nonoptimal concave function, and in the meanvariance setting with the covariance matrix assumed to be given.
We then use the models developed for inverse problem on empirical data to retrieve the implied views implicit in a given portfolio, and attempt to determine whether incorporating these views in portfolio selection improves portfolio performance out of sample.

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